Insurance and Inequality with Persistent Private Information

100 Pages Posted: 27 Dec 2017 Last revised: 21 Sep 2018

See all articles by Alexander W. Bloedel

Alexander W. Bloedel

Stanford University - Department of Economics

R. Vijay Krishna

Florida State University - Department of Economics

Oksana Leukhina

Federal Reserve Bank of St Louis

Multiple version iconThere are 2 versions of this paper

Date Written: September 7, 2018

Abstract

We study optimal insurance contracts for an agent with Markovian private information. Our main results characterize the implications of constrained efficiency for long-run welfare and inequality. Under minimal technical conditions, there is Absolute Immiseration: in the long run, the agent’s consumption and utility converge to their lower bounds. When types are persistent and utility is unbounded below, there is Relative Immiseration: low-type agents are immiserated at a faster rate than high-type agents, and “pathwise welfare inequality” grows without bound. These results extend and substantially generalize the hallmark findings from the classic literature with iid types, suggesting that the underlying forces are robust to a broad class of private information processes. The proofs rely on novel recursive techniques and martingale arguments. When the agent has CARA utility, we also analytically and numerically characterize the short-run properties of the optimal contract. Persistence gives rise to qualitatively novel short-run dynamics and allocative distortions (or “wedges”) and, quantitatively, induces less efficient risk-sharing. We compare properties of the wedges to their counterparts in the dynamic taxation literature.

Keywords: Absolute immiseration, relative immiseration, dynamic contracting, recursive contracts, principal-agent problem, persistent private information

JEL Classification: C73, D30, D31, D80, D82, E61

Suggested Citation

Bloedel, Alexander W. and Krishna, R. Vijay and Leukhina, Oksana, Insurance and Inequality with Persistent Private Information (September 7, 2018). Available at SSRN: https://ssrn.com/abstract=3091457 or http://dx.doi.org/10.2139/ssrn.3091457

Alexander W. Bloedel (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
STANFORD, CA 94305-6072
United States

R. Vijay Krishna

Florida State University - Department of Economics ( email )

Tallahassee, FL 30306-2180
United States

Oksana Leukhina

Federal Reserve Bank of St Louis ( email )

P.O. Box 442
St. Louis, MO 63166-0442
United States

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